Block #556,700

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/22/2014, 11:05:16 AM · Difficulty 10.9627 · 6,252,197 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

493dfbbb7045311144a1a938802718b0cfa4527b14abd3ccf935724aeb80cb8c

View on Chainz ↗

Height

#556,700

Difficulty

10.962693

Transactions

Size

1.30 KB

Version

Bits

0af67306

Nonce

88,573,632

Timestamp

5/22/2014, 11:05:16 AM

Confirmations

6,252,197

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1ac5f27c9f3e0af3f79ddfd959b984ce51b23d06427e9ed4cd956a91f5a38e1b

Transactions (4)

Coinbase4669085d48eca0…056d25d9f884b9

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

35b640967b80ed…0574a6d89d721f

1 in → 2 out5.3549 XPM225 B

AKT4pWwh…ku8k4dSq ATTj3Quj…RogtXXPS

ecee4fb9656d83…e3b9e656208816

1 in → 2 out2.8426 XPM225 B

AXqQKd1j…A9Ae5Z6u AS9ZCvju…bu3NEFwZ

e5395acfbcaf03…8f973af071e16c

4 in → 2 out1.3187 XPM671 B

AKWZwe8L…XpSKrkon AM23VEk3…q622MtoH

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.126 × 10¹⁰¹(102-digit number)

21265412405025985745…54098270664914821119

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.126 × 10¹⁰¹(102-digit number)

21265412405025985745…54098270664914821119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.126 × 10¹⁰¹(102-digit number)

21265412405025985745…54098270664914821121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.253 × 10¹⁰¹(102-digit number)

42530824810051971490…08196541329829642239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.253 × 10¹⁰¹(102-digit number)

42530824810051971490…08196541329829642241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

8.506 × 10¹⁰¹(102-digit number)

85061649620103942981…16393082659659284479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.506 × 10¹⁰¹(102-digit number)

85061649620103942981…16393082659659284481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.701 × 10¹⁰²(103-digit number)

17012329924020788596…32786165319318568959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.701 × 10¹⁰²(103-digit number)

17012329924020788596…32786165319318568961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.402 × 10¹⁰²(103-digit number)

34024659848041577192…65572330638637137919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.402 × 10¹⁰²(103-digit number)

34024659848041577192…65572330638637137921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.804 × 10¹⁰²(103-digit number)

68049319696083154385…31144661277274275839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #556,700

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